Graphene In Strong Magnetic Field Research Articles

Many-body filling factor dependent renormalization of Fermi velocity in graphene in strong magnetic field

We present the theory of many-body corrections to cyclotron transition energies in graphene in strong magnetic field due to Coulomb interaction, considered in terms of the renormalized Fermi velocity. A particular emphasis is made on the recent experiments where detailed dependencies of this velocity on the Landau level filling factor for individual transitions were measured. Taking into account the many-body exchange, excitonic corrections and interaction screening in the static random-phase approximation, we successfully explained the main features of the experimental data, in particular that the Fermi velocities have plateaus when the 0th Landau level is partially filled and rapidly decrease at higher carrier densities due to enhancement of the screening. We also explained the features of the nonmonotonous filling-factor dependence of the Fermi velocity observed in the earlier cyclotron resonance experiment with disordered graphene by taking into account the disorder-induced Landau level broadening.

Many-body renormalization of Landau levels in graphene due to screened Coulomb interaction

Renormalization of Landau level energies in graphene in strong magnetic field due to Coulomb interaction is studied theoretically, and calculations are compared with two experiments on carrier-density dependent scanning tunneling spectroscopy. An approximate preservation of the square-root dependence of the energies of Landau levels on their numbers and magnetic field in the presence of the interaction is examined. Many-body calculations of the renormalized Fermi velocity with the statically screened interaction taken in the random-phase approximation show good agreement with both experiments. The crucial role of the screening in achieving quantitative agreement is found. The main contribution to the observed rapid logarithmic growth of the renormalized Fermi velocity on approach to the charge neutrality point turned out to be caused not by mere exchange interaction effects, but by weakening of the screening at decreasing carrier density. The importance of a self-consistent treatment of the screening is also demonstrated.

SO(8) fermion dynamical symmetry and strongly correlated quantum Hall states in monolayer graphene

A formalism is presented for treating strongly-correlated graphene quantum Hall states in terms of an SO(8) fermion dynamical symmetry that includes pairing as well as particle--hole generators. The graphene SO(8) algebra is isomorphic to an SO(8) algebra that has found broad application in nuclear physics, albeit with physically very different generators, and exhibits a strong formal similarity to SU(4) symmetries that have been proposed to describe high-temperature superconductors. The well-known SU(4) symmetry of quantum Hall ferromagnetism for single-layer graphene is recovered as one subgroup of SO(8), but the dynamical symmetry structure associated with the full set of SO(8) subgroup chains extends quantum Hall ferromagnetism and allows analytical many-body solutions for a rich set of collective states exhibiting spontaneously-broken symmetry that may be important for the low-energy physics of graphene in strong magnetic fields. The SO(8) symmetry permits a natural definition of generalized coherent states that correspond to symmetry-constrained Hartree--Fock--Bogoliubov solutions, or equivalently a microscopically-derived Ginzburg--Landau formalism, exhibiting the interplay between competing spontaneously broken symmetries in determining the ground state.

Nonlinear optics of graphene in a strong magnetic field

Graphene placed in a magnetic field possesses an extremely high mid/far-infrared optical nonlinearity originating from its unusual band structure and selection rules for the optical transitions near the Dirac point. Here, we study the linear and nonlinear optical response of graphene in strong magnetic and optical fields using a quantum-mechanical density-matrix formalism. We calculate the power of the coherent terahertz radiation generated as a result of the four-wave mixing in graphene. We show that even one monolayer of graphene gives rise to an appreciable nonlinear frequency conversion efficiency and Raman gain for modest intensities of the incident infrared radiation.

Chiral condensate with topological degeneracy in graphene and its manifestation in edge states

The role of chiral symmetry in many-body states of graphene in strong magnetic fields is theoretically studied with the honeycomb lattice model. For a spin-split Landau level where the leading electron-electron interaction is the nearest-neighbor repulsion, a chiral condensate is shown to be, within the subspace of the $n=0$ Landau level, an exact many-body ground state having a finite gap, for which a calculation of the Chern number reveals that the ground state is a Hall insulator with a topological degeneracy of two. The topological nature of the ground state is shown to manifest itself as a Kekul\'ean bond order along armchair edges, while the pattern melts in the bulk due to quantum fluctuations. These can be regarded as a realization of the bulk-edge correspondence that is peculiar to a chiral-symmetric system. We have also obtained the ground state when point defects are introduced in the honeycomb lattice to reveal how the presence or absence of the chiral symmetry affects the defect states.

Influence of Landau level mixing on the properties of elementary excitations in graphene in strong magnetic field

Massless Dirac electrons in graphene fill Landau levels with energies scaled as square roots of their numbers. Coulomb interaction between electrons leads to mixing of different Landau levels. The relative strength of this interaction depends only on dielectric susceptibility of surrounding medium and can be large in suspended graphene. We consider influence of Landau level mixing on the properties of magnetoexcitons and magnetoplasmons—elementary electron-hole excitations in graphene in quantizing magnetic field. We show that, at small enough background dielectric screening, the mixing leads to very essential change of magnetoexciton and magnetoplasmon dispersion laws in comparison with the lowest Landau level approximation.PACS: 73.22.Pr; 71.35.Ji; 73.43.Mp; 71.70.Gm.

Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels (LLs) in the integer quantum Hall (QH) effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher LLs, taking into account the LL mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the dependence of the gap parameters on the LL index n (‘running’ gaps). The renormalization (running) of the Fermi velocity as a function of n is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer QH plateaus in graphene in strong magnetic fields.

Landau-level broadening due to electron-impurity interaction in graphene in strong magnetic fields

The effect of electron-impurity and electron-electron interactions on the energy spectrum of electrons moving in graphene is investigated in the presence of a high magnetic field. We find that the width of the broadened Landau levels exhibits an approximate $1/B$ dependence near half filling for charged impurity scattering. The Landau-level width, the density of states, and the Fermi energy exhibit an oscillatory behavior as a function of magnetic field. Comparison with experiment shows that scattering with charged impurities cannot be the main scattering mechanism that determines the width of the Landau levels.

Publisher's Note: Localized collective excitations in doped graphene in strong magnetic fields [Phys. Rev. B80, 165410 (2009)

Received 26 October 2009DOI:https://doi.org/10.1103/PhysRevB.80.169906©2009 American Physical Society

Localized collective excitations in doped graphene in strong magnetic fields

We consider collective excitations in graphene with filled Landau levels (LL's) in the presence of an external potential due to a single charged donor D{sup +} or acceptor A{sup -} impurity. We show that localized collective modes split off the magnetoplasmon continuum and, in addition, quasibound states are formed within the continuum. A study of the evolution of the strengths and energies of magneto-optical transitions is performed for integer filling factors {nu}=1,2,3,4 of the lowest LL. We predict impurity absorption peaks above as well as below the cyclotron resonance. We find that the single-particle electron-hole symmetry of graphene leads to a duality between the spectra of collective modes for the D{sup +} and A{sup -}. The duality shows up as a set of the D{sup +} and A{sup -} magnetoabsorption peaks having the same energies but active in different circular polarizations.

Onset of an Insulating Zero-Plateau Quantum Hall State in Graphene

We analyze the dissipative conductance of the zero-plateau quantum Hall state appearing in undoped graphene in strong magnetic fields. Charge transport in this state is assumed to be carried by a magnetic domain wall, which forms by hybridization of two counterpropagating edge states of opposing spin due to interactions. The resulting nonchiral edge mode is a Luttinger liquid of parameter K, which enters a gapped, perfectly conducting state below a critical value K_{c} approximately 1/2. Backscattering in this system involves spin flip, so that interaction with localized magnetic moments generates a finite resistivity Rxx via a "chiral Kondo effect." At finite temperatures T, Rxx(T) exhibits a crossover from metallic to insulating behavior as K is tuned across a threshold K_{MI}. For T --> 0, Rxx in the intermediate regime K_{MI} < K < K_{c} is finite, but diverges as K approaches K_{c}. This model provides a natural interpretation of recent experiments.

DYNAMICAL GAPS AND QUANTUM HALL EFFECT IN GRAPHENE

We analyze the gap equation for Dirac quasiparticles in graphene in a magnetic field using a low-energy effective model with a contact interaction. It is found that the order parameters connected with the quantum Hall (QH) ferromagnetism and the magnetic catalysis scenarios necessarily coexist. The ground-state solutions of the gap equation describe all the recently discovered novel QH plateaus in graphene in strong magnetic fields.

Toward a theory of the quantum Hall effect in graphene

We analyze a gap equation for the propagator of Dirac quasiparticles and conclude that in graphene in a magnetic field, the order parameters connected with the quantum Hall ferromagnetism dynamics and those connected with the magnetic catalysis dynamics necessarily coexist (the latter have the form of Dirac masses and correspond to excitonic condensates). This feature of graphene could lead to important consequences, in particular, for the existence of gapless edge states. Solutions of the gap equation corresponding to recently experimentally discovered novel plateaus in graphene in strong magnetic fields are described.

Dynamics in the quantum Hall effect and the phase diagram of graphene

The dynamics responsible for lifting the degeneracy of the Landau levels in the quantum Hall (QH) effect in graphene is studied by utilizing a low-energy effective model with a contact interaction. A detailed analysis of the solutions of the gap equation for Dirac quasiparticles is performed at both zero and nonzero temperatures. The characteristic feature of the solutions is that the order parameters connected with the QH ferromagnetism and magnetic catalysis scenarios necessarily coexist. The solutions reproduce correctly the experimentally observed QH plateaus in graphene in strong magnetic fields. The phase diagram of this system in the plane of temperature and electron chemical potential is analyzed. The phase transitions corresponding to the transitions between different QH plateaus in graphene are described.